CN117715186B - AoA positioning method based on RNDAC-ZNN model - Google Patents

AoA positioning method based on RNDAC-ZNN model Download PDF

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CN117715186B
CN117715186B CN202410167331.8A CN202410167331A CN117715186B CN 117715186 B CN117715186 B CN 117715186B CN 202410167331 A CN202410167331 A CN 202410167331A CN 117715186 B CN117715186 B CN 117715186B
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rndac
znn
base station
positioning method
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CN117715186A (en
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邹利兰
庄豐豪
林聪�
蔡东耀
陈欣桐
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Guangdong Ocean University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S11/00—Systems for determining distance or velocity not using reflection or reradiation
    • G01S11/02—Systems for determining distance or velocity not using reflection or reradiation using radio waves
    • G01S11/04—Systems for determining distance or velocity not using reflection or reradiation using radio waves using angle measurements
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/12—Simultaneous equations, e.g. systems of linear equations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/02—Services making use of location information
    • H04W4/023—Services making use of location information using mutual or relative location information between multiple location based services [LBS] targets or of distance thresholds

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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Data Mining & Analysis (AREA)
  • Theoretical Computer Science (AREA)
  • Algebra (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Computing Systems (AREA)
  • Operations Research (AREA)
  • Position Fixing By Use Of Radio Waves (AREA)

Abstract

The application discloses an AoA positioning method based on RNDAC-ZNN model, which comprises the following steps: forming a linear equation set about the coordinate equation based on the position coordinates of the i base station to the j base station; constructing a RNDAC-ZNN model based on the original NZNN model; based on the RNDAC-ZNN model, solving the linear equation set to obtain a solution about the target position, the method provided by the application overcomes the defect that the AoA positioning method cannot realize global convergence under the noise interference condition, and greatly improves the accurate solving performance of the model under the noise interference condition.

Description

AoA positioning method based on RNDAC-ZNN model
Technical Field
The invention relates to the technical field of AoA positioning, in particular to an AoA positioning method based on RNDAC-ZNN model.
Background
Theoretically, positioning can be achieved by obtaining information such as TOA, AOA, and AOD of the signal, which can be obtained by channel state information. Considering sparse features of millimeter wave channels, many millimeter wave positioning algorithms are based on compressed sensing expansion.
Channel noise is one of the unavoidable factors affecting the performance of a communication system, and in order to achieve high-precision positioning, it is desirable to reduce as much as possible its interference to the channel estimation process. In the prior art, the ZNN models are used for eliminating interference, but the models are initial models or models with nonlinear activation functions and have less residual information, so that the convergence speed of the models is low, the interference resistance is not strong, and the positioning accuracy of user equipment and a base station is seriously affected.
Disclosure of Invention
Aiming at the prior art, the invention aims to provide an AoA positioning method based on RNDAC-ZNN model, which mainly solves the technical problems in the background art.
In order to achieve the above object, the technical solution of the embodiment of the present invention is as follows: an AoA positioning method based on RNDAC-ZNN model, the positioning method comprising:
Forming a linear equation set about the coordinate equation based on the position coordinates of the i base station to the j base station;
constructing a RNDAC-ZNN model based on the original NZNN model;
And solving the linear equation system based on the RNDAC-ZNN model to obtain a solution about the target position.
Optionally, the incident angle of the jth base station is set asThe pitch angle is/>The position coordinate of the jth base station is/>Where j belongs to 1,2, 3..n, n is a constant, and the coordinate equation thus formed is:
Wherein the method comprises the steps of Is a calculation parameter related to the distance from the base station to the origin of the virtual three-dimensional coordinate system, wherein the value of n is constant.
Optionally, the method for converting the coordinate equation into the linear equation set specifically includes:
Will be Expressed as/>Will/>Expressed as/>Will beExpressed as/>Thus, the linear equation is formed as: /(I)And define its error function as/>Wherein/>Representing the error function of the aforementioned linear equation.
Optionally, the RNDAC-ZNN model is constructed as follows:
wherein, To adjust the coefficient,/>Is a feedback coefficient,/>Representing an adaptive control function,/>Representing an adaptive feedback activation function,/>The element of the transition representing time t,/>Representation/>Is a function of the integral of (a).
Optionally, the adaptive control function includes a power bounded adaptive function and an exponent bounded adaptive function.
Optionally, solving the linear equation set based on the RNDAC-ZNN model specifically includes: bringing the expression of RNDAC-ZNN model into the error function of a system of linear equationsIn (1), obtaining:
Wherein the method comprises the steps of For/>After bringing in a specific numerical value of the coordinates, find the first derivative form of (i) with respect to/>The solution of/>The solution of (a) is the AoA positioning result.
The application has the beneficial effects that: the AoA positioning method based on RNDAC-ZNN model provided by the application comprises the steps of 1. Using RNDAC-ZNN model integrating various residual information, obviously enhancing the convergence performance of AoA and improving the convergence speed, and under the condition of enough calculation power, RNDAC has stronger timeliness; 2. the AoA positioning method based on RNDAC-ZNN model overcomes the defect that the AoA positioning method cannot realize global convergence under the condition of noise interference, and greatly improves the performance of accurately solving the model under the condition of noise interference; 3. compared with the method that some models are converted into non-time-varying or the time-invariant problem is assumed to be solved within a period of time, the AoA positioning method based on the RNDAC-ZNN model considers that the environment to be actually solved uses a time-varying equation, so that the influence of environmental parameters and time hysteresis errors in the actual solving process are avoided; 4. the three-dimensional AoA positioning problem is converted into a mathematical linear time-varying matrix decomposition and zero finding problem to be solved, the solving difficulty is reduced, and the positioning accuracy of the proposed model is higher.
Drawings
Fig. 1 is a flow chart of an AoA positioning method based on RNDAC-ZNN model in an embodiment of the present application;
Fig. 2 is a schematic diagram of a 3D-AoA positioning method according to an embodiment of the present application;
FIG. 3 is a diagram showing a comparison of actual solution and theoretical solution paths RNDAC-ZNN in an embodiment of the present application;
FIG. 4 is a graph showing comparison of error norms RNDAC-ZNN and OZNN, NTZNN, NZNN in an embodiment of the present application;
FIG. 5 is a diagram of a real-time position error for RNDAC-ZNN to resolve AoA positioning in an embodiment of the present application;
fig. 6 is a graph of error norms for RNDAC-ZNN to resolve AoA positioning under various noise conditions in an embodiment of the present application.
Detailed Description
The technical scheme of the invention is further elaborated below by referring to the drawings in the specification and the specific embodiments. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. In the following description, reference is made to the expression "some embodiments" which describe a subset of all possible embodiments, but it should be understood that "some embodiments" may be the same subset or a different subset of all possible embodiments and may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a more thorough understanding of the present invention. It will be apparent, however, to one skilled in the art that the invention may be practiced without one or more of these details. In other instances, well-known features have not been described in detail in order to avoid obscuring the invention.
It should be understood that the present invention may be embodied in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. And the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. As used herein, the term "and/or" includes any and all combinations of the associated listed items.
It will be further understood that when an element is referred to as being "fixed to" another element, it can be directly on the other element or intervening elements may also be present. When an element is referred to as being "connected" to another element, it can be directly connected to the other element or intervening elements may also be present. The terms "vertical," "horizontal," "inner," "outer," "left," "right," and the like are used herein for illustrative purposes only and are not meant to be the only embodiment.
In order to provide a thorough understanding of the present invention, detailed structures will be presented in the following description in order to illustrate the technical solutions presented by the present invention. Alternative embodiments of the invention are described in detail below, however, the invention may have other implementations in addition to these detailed descriptions.
Referring to fig. 1 in combination, the present application provides an AoA positioning method based on RNDAC-ZNN model, the positioning method includes:
S1, forming a linear equation set about a coordinate equation based on position coordinates of an ith base station to a jth base station;
s2, constructing a RNDAC-ZNN model based on an original NZNN model;
And S3, solving the linear equation set based on the RNDAC-ZNN model to obtain a solution about the target position.
Specifically, the incident angle of the jth base station is set asThe pitch angle is/>The position coordinate of the jth base station is/>Where j belongs to 1,2, 3..n, n is a constant, and the coordinate equation thus formed is:
Wherein the method comprises the steps of Is a calculation parameter related to the distance from the base station to the origin of the virtual three-dimensional coordinate system, wherein the value of n is constant.
Further, the method for converting the coordinate equation into the linear equation set specifically includes:
Will be Expressed as/>Will/>Expressed as/>Will beExpressed as/>Thus, the linear equation is formed as: /(I)And define its error function as/>Wherein/>Representing the error function of the aforementioned linear equation.
Specifically, the RNDAC-ZNN model is constructed as follows:
wherein, To adjust the coefficient,/>Is a feedback coefficient,/>Representing an adaptive control function,/>Representing an adaptive feedback activation function,/>The element of the transition representing time t,/>Representation/>Is a function of the integral of (a).
In some embodiments of the present application, the built RNDAC-ZNN model can be used to solve LR decomposition problems and QR decomposition problems in practical application, the LR decomposition can be applied to image watermarking, finite difference and finite element methods, recursive segmentation algorithms, etc., and many problems in engineering can be solved by converting the LR decomposition into LR decomposition, which shows superior decomposition characteristics and reduces many calculation amounts, such as research on parallel operations. QR decomposition can be applied to pseudo-inverse computation of matrices, least squares fitting, and is applied in real life to adaptive beamformers for ultrasound imaging.
For example, the RNDAC-ZNN model is deformed into the form of the RNDAC-LZNN model when solving the LR decomposition problem, and the evolution formula is as follows:
Order the The following equation can be obtained:
Vectorization is performed on the above results in:
Order the RNDAC-LZNN are given as:
The noise model is as follows:
When the RNDAC-ZNN model solves the problem of QR solution, the model is deformed into a RNDAC-LZNN form, and an evolution formula is as follows:
Order the The following equation can be obtained: /(I)
Vectorization is performed on the above results in:
converting the above formula into a matrix form, then RNDAC-QZNN model can be changed into:
The noise model is as follows:
further, the adaptive control function includes a power bounded adaptive function and an exponent bounded adaptive function.
Wherein the power bounded adaptive function is expressed as:
The expression of the exponential bounded adaptive function is:
In both cases, where i, j=1, 2,..n, where And/>Is a positive parameter defining an upper bound and a lower bound, controlling the behavior of the function within the bounds. Parameter/>Is adjusted to limit the residual error of the solution system and to enhance its robustness. Parameter/>And/>Is a super parameter for controlling convergence speed
Specifically, for the linear equation: It/> ，，/>QR decomposition/>The method comprises the following steps:
wherein, Is an orthogonal matrix,/>Is an upper triangular matrix, which is composed of orthogonal moment
The array properties are:
Wherein the method comprises the steps of Represents an upper triangular matrix, 0 represents a zero matrix,/>Representing the rank of B.
Order theThe method can obtain:
Based on the solving process of the general solution, the expression of RNDAC-ZNN model is brought into an error function of a linear equation set In (1), obtaining:
Wherein the method comprises the steps of For/>After bringing in a specific numerical value of the coordinates, find the first derivative form of (i) with respect to/>The solution of/>The solution of (a) is the AoA positioning result.
In order to verify the effect of the present application, the present application further provides a process of designing and executing a verification experiment, such as fig. 2, which shows a solid model of the AoA positioning method.
For experimental needs, OZNN models are given:
，
NTZNN model:
，
N-Acf activated NZNN:
,
wherein the N-Acf activation function is:
and (3) experimental parameter design: ,/>，/>，/> and the initial states of the models are randomly generated.
Wherein the activation function used to design RNDAC-ZNN
Power bounded adaptive function:
Exponential bounded adaptive function:
In this experimental example, the moving path of the moving object is:
the number of base stations in the computer simulation experiment was set to 2. Their locations were AndThe path solved by RNDAC-ZNN model in AoA positioning in FIG. 3 indicates that the actual path and the path trajectory are almost completely unified, and the fitting degree is extremely high. In FIG. 4, the steady state error convergence upper and lower bounds of RNDAC are most accurate in comparison to OZNN, NTZNN, NZNN error, indicating that the solution location of RNDAC-ZNN is at/>, in real timeOn the order of magnitude of (2).
Experiments under noise conditions were designed for the integrity of the experiments and the robustness of the performance model. Wherein the constant noise is [5; 5] (the variation range of the bounded random noise is [ -2,2]; the linear time-varying noise is t, t and t. FIG. 6 shows that RNDAC-ZNN has an error steady-state norm under various noise conditions, which shows that RNDAC-ZNN has strong noise immunity under the influence of noise, and the solving process under the influence of environment has almost no influence on RNDAC-ZNN, so that the strong robustness of the RNDAC-ZNN model to AoA solving is proved, the AoA positioning method based on the RNDAC-ZNN model has high convergence rate, and the CPU solving time is equal to about 0.1s convergence. Under the condition of enough calculation force, RNDAC has stronger timeliness.
The foregoing is merely illustrative embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily think about variations or substitutions within the technical scope of the present invention, and the invention should be covered. The scope of the invention is to be determined by the appended claims.

Claims (4)

1. An AoA positioning method based on RNDAC-ZNN model, which is characterized by comprising the following steps:
Forming a linear equation set about the coordinate equation based on the position coordinates of the i base station to the j base station;
Based on an original NZNN model, constructing a RNDAC-ZNN model, wherein a NZNN model represents a nonlinear activated zero-ized neural network, and a RNDAC-ZNN model represents a robust neural dynamics-zero-ized neural network with an adaptive coefficient function;
solving the linear equation set based on the RNDAC-ZNN model to obtain a solution for the target location;
Setting the incident angle of the jth base station as The pitch angle is/>The position coordinate of the jth base station isWhere j belongs to 1,2, 3..n, n is a constant, and the coordinate equation thus formed is:
Wherein the method comprises the steps of Is a calculation parameter related to the distance from the base station to the origin of the virtual three-dimensional coordinate system, wherein the value of n is constant, t is a time value,/>Represents the incident angle of the nth base station,/>、/>、/>Representing the position coordinates;
The RNDAC-ZNN model is constructed as follows:
wherein, To adjust the coefficient,/>Is a feedback coefficient,/>Representing an adaptive control function,/>Representing an adaptive feedback activation function,/>The element of the transition representing time t,/>Representation/>Integral of/(I)The error function representing the model, i, j, is constant.
2. The AoA positioning method based on RNDAC-ZNN model according to claim 1, wherein the transformation of the coordinate equation into a linear equation set specifically includes:
Will be Expressed as/>Will/>Expressed as/>Will beExpressed as/>Thus, the linear equation is formed as: /(I)And define its error function as/>Wherein/>Representing the error function of the aforementioned linear equation.
3. An AoA positioning method based on RNDAC-ZNN model according to claim 2, wherein the adaptive control functions include power-bounded adaptive functions and exponent-bounded adaptive functions.
4. An AoA positioning method based on RNDAC-ZNN model according to claim 3, wherein solving the system of linear equations based on the RNDAC-ZNN model specifically includes: bringing the expression of RNDAC-ZNN model into the error function of a system of linear equationsIn (1), obtaining:
Wherein the method comprises the steps of For/>After bringing in a specific numerical value of the coordinates, find the first derivative form of (i) with respect to/>Solutions concerning/>The solution of (a) is the AoA positioning result.
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CN117930135B (en) * 2024-03-21 2024-08-16 广东海洋大学 TDOA moving target positioning method based on NRZND model
CN117930136B (en) * 2024-03-21 2024-06-21 广东海洋大学 Multi-mobile sound source positioning method based on self-adaptive complex value return-to-zero neural dynamics

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